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Chaotic Hopfield neural network swarm optimization and its application. (English) Zbl 1266.37053

Summary: A new neural network based optimization algorithm is proposed. The presented model is a discrete-time, continuous-state Hopfield neural network and the states of the model are updated synchronously. The proposed algorithm combines the advantages of traditional PSO, chaos and Hopfield neural networks: particles learn from their own experience and the experiences of surrounding particles, their search behavior is ergodic, and convergence of the swarm is guaranteed. The effectiveness of the proposed approach is demonstrated using simulations and typical optimization problems.

MSC:

37N25 Dynamical systems in biology
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[1] J. C. Sprott, Chaos and Time-Series Analysis, Oxford University Press, New York, NY, USA, 2004. · Zbl 1201.91171
[2] K. Aihara and G. Matsumoto, Chaos in Biological Systems, Plenum Press, New York, NY, USA, 1987.
[3] C. A. Skarda and W. J. Freeman, “How brains make chaos in order to make sense of the world,” Behavioral and Brain Sciences, vol. 10, pp. 161-165, 1987.
[4] L. Wang, D. Z. Zheng, and Q. S. Lin, “Survey on chaotic optimization methods,” Computation Technology Automation, vol. 20, pp. 1-5, 2001.
[5] B. Li and W. S. Jiang, “Optimizing complex functions by chaos search,” Cybernetics and Systems, vol. 29, no. 4, pp. 409-419, 1998. · Zbl 1012.90068
[6] J. J. Hopfield and D. W. Tank, “‘Neural’ computation of decisons in optimization problems,” Biological Cybernetics, vol. 52, no. 3, pp. 141-152, 1985. · Zbl 0572.68041
[7] Z. Wang, Y. Liu, K. Fraser, and X. Liu, “Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays,” Physics Letters A, vol. 354, no. 4, pp. 288-297, 2006. · Zbl 1181.93068
[8] T. Tanaka and E. Hiura, “Computational abilities of a chaotic neural network,” Physics Letters A, vol. 315, no. 3-4, pp. 225-230, 2003. · Zbl 1046.68093
[9] K. Aihara, T. Takabe, and M. Toyoda, “Chaotic neural networks,” Physics Letters A, vol. 144, no. 6-7, pp. 333-340, 1990.
[10] S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, no. 4598, pp. 671-680, 1983. · Zbl 1225.90162
[11] L. Chen and K. Aihara, “Chaotic simulated annealing by a neural network model with transient chaos,” Neural Networks, vol. 8, no. 6, pp. 915-930, 1995. · Zbl 05479122
[12] L. Chen and K. Aihara, “Chaos and asymptotical stability in discrete-time neural networks,” Physica D, vol. 104, no. 3-4, pp. 286-325, 1997. · Zbl 0889.68122
[13] L. Wang, “On competitive learning,” IEEE Transactions on Neural Networks, vol. 8, no. 5, pp. 1214-1217, 1997.
[14] L. Wang and K. Smith, “On chaotic simulated annealing,” IEEE Transactions on Neural Networks, vol. 9, no. 4, pp. 716-718, 1998.
[15] M. Clerc and J. Kennedy, “The particle swarm-explosion, stability, and convergence in a multidimensional complex space,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 1, pp. 58-73, 2002. · Zbl 05451976
[16] J. Ke, J. X. Qian, and Y. Z. Qiao, “A modified particle swarm optimization algorithm,,” Journal of Circuits and Systems, vol. 10, pp. 87-91, 2003.
[17] B. Liu, L. Wang, Y. H. Jin, F. Tang, and D. X. Huang, “Improved particle swarm optimization combined with chaos,” Chaos, Solitons and Fractals, vol. 25, no. 5, pp. 1261-1271, 2005. · Zbl 1074.90564
[18] T. Xiang, X. Liao, and K. W. Wong, “An improved particle swarm optimization algorithm combined with piecewise linear chaotic map,” Applied Mathematics and Computation, vol. 190, no. 2, pp. 1637-1645, 2007. · Zbl 1122.65363
[19] C. Fan and G. Jiang, “A simple particle swarm optimization combined with chaotic search,” in Proceedings of the 7th World Congress on Intelligent Control and Automation (WCICA ’08), pp. 593-598, Chongqing, China, June 2008.
[20] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, pp. 1942-1948, Perth, Australia, December 1995.
[21] S. H. Chen, A. J. Jakeman, and J. P. Norton, “Artificial Intelligence techniques: an introduction to their use for modelling environmental systems,” Mathematics and Computers in Simulation, vol. 78, no. 2-3, pp. 379-400, 2008. · Zbl 1140.68507
[22] J. J. Hopfield, “Hopfield network,” Scholarpedia, vol. 2, article 1977, 2007.
[23] J. J. Hopfield, “Neurons with graded response have collective computational properties like those of two-state neurons,” Proceedings of the National Academy of Sciences of the United States of America, vol. 81, no. 10, pp. 2554-2558, 1984. · Zbl 1371.92015
[24] Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J. C. Hernandez, and R. G. Harley, “Particle swarm optimization: basic concepts, variants and applications in power systems,” IEEE Transactions on Evolutionary Computation, vol. 12, no. 2, pp. 171-195, 2008. · Zbl 05516173
[25] J. D. Schaffer, R. A. Caruana, L. J. Eshelman, and R. Das, “A study of control parameters affectiong online performance of genetic algorithms for function optimization,” in Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 51-60, 1989.
[26] A. I. de Freitas Vaz and E. M. da Gra\cca Pinto Fernandes, “Optimization of nonlinear constrained particle swarm,” Technological and Economic Development of Economy, vol. 12, no. 1, pp. 30-36, 2006.
[27] X. Hu, R. C. Eberhart, and Y. Shi, “Engineering optimization with particle swarm,” in Proceedings of the IEEE Swarm Intelligence Symposium, pp. 53-57, 2003.
[28] C. A. C. Coello, “Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 11-12, pp. 1245-1287, 2002. · Zbl 1026.74056
[29] J. Kennedy, “Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance,” Neural Networks, vol. 18, pp. 205-217, 1997.
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